Initially Teamviewer detected a commercial use of the software. I was sure that this was wrong and so I contacted teamviewer via their homepage and filled out the form for suspected commercial use. I mentioned all IDs of the computers I usually connect to as well as my own ID. After a few days I received an e-mail informing me that my teamviewer ID was set to private again. I just finished the first session after the reset and everything works great and as expected again. Thank you for your help and a great software!
